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pi Formula for pi/4 created by Leibniz.

Leibniz formula for pi

k=0(1)k2k+1=π4 {\displaystyle \sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2k+1}}}=\frac{\pi}{4}

{% hint style="info" %} Curiously, despite being named Leibniz's formula for pi, this formula was not actually created by Leibniz. Bernoulli who was Leibniz's teacher and mentor discovered it; the book was then worked on and published by both of them. Leibniz had a curious arrangement with his teacher in which he bought all mathematical discoveries made by his teacher. {% endhint %}

Proof